Two spheres

Electricity and Magnetism Level 1

In what ratio will a charge split up between two conductive spheres connected with a long thin wire ?

Details and assumptions:

The radii of the two spheres are $r_1 = 7 \space \text{cm}$ and $r_2 = 3 \space \text{cm}$ .
The wire is long and thin enough, so that it doesn't disturb the even distribution on both spheres, the charge splits up so that their potential is the same.
Give your ratio as the larger sphere to the smaller sphere.
Give your answer to 2 decimal places.

The answer is 2.33.

1 solution

André Hucek
Oct 18, 2017

We see that

$\displaystyle \frac{Q_1}{4 \pi \varepsilon \varepsilon_0} \frac{1}{r_1} = \frac{Q_2}{4 \pi \varepsilon \varepsilon_0} \frac{1}{r_2}$ From which

$\displaystyle \frac{Q_1}{Q_2} = \frac{r_1}{r_2} = \frac{7}{3} = \boxed{2.33}$

So the charge splits up in the ratio of the radii: $70\%$ on the larger sphere, $30\%$ on the smaller sphere.

You might want to specify whether the ratio is q1/q2 or q2/q1. People might get the answer wrong for a silly reason otherwise.

Steven Chase - 3 years, 7 months ago

Given that $\color{#3D99F6}r_1 = 7$ and $\color{#D61F06}r_2 = 3$ , and that $\frac{Q_1}{Q_2} = \frac{\color{#3D99F6}{r_1}}{\color{#D61F06}{r_2}}$ , it is unlikely to be switched, but i will edit it, thank you for your feedback.

André Hucek - 3 years, 7 months ago

Two spheres

The answer is 2.33.

1 solution

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